Step by step
The question
Question: find x.
An isosceles triangle has top angle x and base angle x + 30.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two.
Fold it on the dashed line, from the top to the middle of the base.
The two halves fit exactly.
So the two angles at the base fit on each other.
The base angles are equal.
So the other base angle is x + 30 too.
2 Use the angle fact
The three angles in a triangle add up to 180°: x + x + 30 + x + 30 = 180.
Careful!
There are two base angles.
Both go in the sum.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
Plain numbers go together.
x + x + x = 3x.
30 + 30 = 60.
Now we have 3x + 60 = 180.
We want x by itself.
Two things are stuck to x: times 3 and + 60.
The + 60 is on the outside, so it comes off first.
Then the times 3.
4 Remove the + 60
To remove + 60, we take away 60.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
+ 60 and − 60 make zero.
Cross them out.
180 − 60 = 120.
Now we have 3x = 120.
5 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
120 divided by 3 is 40.
So x = 40!
6 Check
Let's check: put x = 40 back and add the three angles.
They add up to 180°.
So x = 40 is right!
Let's look back.
First: use the isosceles fact.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 60.
Then: remove the 3.
Last: check.